Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof of Sequences: Orders and Representations

  1. Sep 18, 2004 #1
    Hello all

    Let us say we are given a sequence of order 2. By order 2 I mean that we have a sequence in which the differences between the terms forms a sequence of order 1, which has a constant difference between terms. How can I prove that the nth term of a sequence of order 2 can be represented as:

    an^2 + bn + c?

    Or more generally how would I prove that that the nth term of a sequence of order k can be represented as:

    an^k + bn^k-1 +.... + pn + q?

    Any help would we greatly appreciated.

  2. jcsd
  3. Sep 18, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    I think you only need to focus on the highest order term. Just look at the difference [itex]P(n+1) - P(n)[/itex] where P(n) is your sequence and use the first term in the binomial expansion of [itex]P(n+1)[/itex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook